In the present paper, we evaluate analyticaly the
conductance of graphite in the infrared region of the photon
frequencies. It is known that the low energy electron excitations
in graphene can be described very well with the
Slonczewski-Weiss-McClure theory [1]}. The largest
parameter of the theory, \(\gamma _0=3.1\)  eV [2]}, describes
the electron dispersion for in-layer directions \({\bf k}\) . If the
photon energy is less than \(\gamma _0\) , we can use the linear
expansion of the in-layer hopping term in the Hamiltonian and
introduce the constant velocity parameter \(v=10^8\)  cm/s. The
second parameter in the rang is the interlayer hopping \(\gamma _1\) 
of the order of 0.4 eV which is known from experiments on bilayer
graphene [3]}, [4]}. The parameters \(\gamma _3\)  and \(\gamma _4\) 
give the corrections of the order of 10% to the in-layer
velocity \(v\) . The electron-hole overlap of the order of 0.02 eV is
determined by parameters \(\gamma _2\)  and \(\gamma _5\)  (see Fig.
REF ). Therefore, for the photon frequencies larger than 0.1
eV, we can neglect the terms with \(\gamma _2\)  and \(\gamma _5\) .
Calculating
such the integral property as conductivity in the
region of the infrared frequencies between 0.1 eV and 1.5 eV, we can, first, neglect the small parameters of the theory and, second, use
the \(k\) -expansion of the in-layer hopping term. Our results have
the evident analytic form.
